Of course do both. However, in this discussion, you are skewed way off in one direction - promoting polygyny - to the point that you are all-but-ignoring the unrighteousness of the situation, and thinking in a complete fantasy world where you assume all can be fixed with a wife-spanking. Another common theme for you.
Basically, just because it could potentially involve polygamy, you think it's great, and all the other details just have to be fixed in the simplest imaginable way. You are over-focussed on polygamy.
First, second wife is blessing. Remember, this guy is almost running away from blessing. WTF?
Second, what is wrong with his natural insticts? Whole problem exists because he avoids his insticts. I'm sorry, but wife is absolutely right here.
Third, there is trust issue which wife is working on.
Fourth, regarding authority. Spanking isn't "solution for everything", but in this case it will establish authority.
Five, he could easily fix whole issue just by:
1. Demand wife to stop sleeping with another women if this was done and is his will
2. If he think acquintance needs deeper checking do speed evaluation. He already knows her, so he can skip some steps.
It's unlikely acquitance is totally incompatible with wife. Radical feminists and tradwives aren't part of same social circle.
If he already likes acquitance he can just accept her as second wife and restore trust with first. And if he is neutral on acquitance, his insticts should be telling him potential another wife which should move him from my bad unfaithul wife towards messy potential situation (in sense trust restoratiom and what with acquitance) which will at least restore his marriage instead of having current mess.
6. Regarding lesbianism. C'mon, which man didn't dream of threesome? From all sexual situations husband/wife can do with another person this is least threat to their marriage. It's even less threathing than him finding new potential wife and going throught courtship ritual. He should sense that at least.
7. While you are here focused on authority and rightneousness, I'm most interested how to fix whole mess. Restoring authority and restoring trust is rather easy: wife will give him "I'm sorry", promise hellfire for repeating situation, give rather stern warning now or slight punishment to restore authority and demand activites which would restore trust (like wife informing him about everything she does with all other people) with wife's acceptance of control. Consistency of control is hardest part here.
Real issuse, according to me, isn't breaking wife's breaking authority (fixable as per above). It's his lack of trust in his insticts. At worst case they get divorced because wife has cheated him with another women. Hello, this is what is coming if his mind stay on her activities.
If his mind gets washed in proper testosterone dosage, it will move from wife's activities and toward does he wants acquitance as second wife. If yes, simple. If no, then wife needs education in his taste.
Any damage by sin, if done here, can't stopped by stopping sin. Stopping sin only stops additional damage. Only thing which matters now is what to do because now we have to create future. What's point of focusing on wrongdoing. Point of forgiveness is stop brain rumination of past wrongdoings.
Son, your ideas about relationships are going to need some refining.
Proper social wording is gentlemen. At 35 I'm too old to be called son except by my father.
What they say about war, “no plan survives first contact with the enemy”, is very apropos for your approach to the circumstance in question.
There is deeper reasoning behind.
This is a very messed up situation. While it isn't adultery proper, it is sexual misconduct. An analogous situation might be a husband going to prostitutes behind his wife's back. It isn't adultery proper since the prostitutes aren't married women, but it is still a serious problem for a number of reasons.
There is no analogus situation because woman-woman party time can never result in another child, whole any man-woman party time can.